A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints
dc.contributor.author | Barvinok, Alexander I. | en_US |
dc.date.accessioned | 2006-09-08T20:19:30Z | |
dc.date.available | 2006-09-08T20:19:30Z | |
dc.date.issued | 2001-01 | en_US |
dc.identifier.citation | Barvinok, A.; (2001). "A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints ." Discrete & Computational Geometry 25(1): 23-31. <http://hdl.handle.net/2027.42/42424> | en_US |
dc.identifier.issn | 0179-5376 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42424 | |
dc.description.abstract | Let K n be the cone of positive semidefinite n X n matrices and let Å be an affine subspace of the space of symmetric matrices such that the intersection K n ∩Å is nonempty and bounded. Suppose that n ≥ 3 and that codim Å = r+2 choose 2 for some 1 ≤ r ≤ n-2 . Then there is a matrix X ∈ K n ∩Å such that rank X ≤ r . We give a short geometric proof of this result, use it to improve a bound on realizability of weighted graphs as graphs of distances between points in Euclidean space, and describe its relation to theorems of Bohnenblust, Friedland and Loewy, and Au-Yeung and Poon. | en_US |
dc.format.extent | 69338 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag; 2000 Springer-Verlag New York | en_US |
dc.subject.other | Legacy | en_US |
dc.title | A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA barvinok@math.lsa.umich.edu, US | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42424/1/454-25-1-23_10074.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s004540010074 | en_US |
dc.identifier.source | Discrete & Computational Geometry | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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